What is the longest time to expiration for call option you have seen? Where (globally) have you heard of call option expiring in more than 70 years? What is the delta for extremely long call option (at the money)?
This sounds like a homework/exam question.
What do YOU think the delta for an at the money long dated call option is? What’s the delta of an at the money short dated call option?
i’d have to go with the delta = 1, as T really has no effect on the price of the option at that point and the option would likely costly nearly as much as the stock itself. i.e. the return assuming 3% inflation and 0% return over 70 years is 700% alone. add a 5% equity return over that time frame and you’re looking at a 21,800%+ return, making the current stock price negligable. i have no input for the other two questions.
Delta never equals 1 for at-the-money options unless it’s within minutes of expiration, otherwise the option would be priced at 0. Options on index futures can have long-dated contracts that expire almost a decade from now.
JohnThainsLimoDriver Wrote: ------------------------------------------------------- > Delta never equals 1 for at-the-money options > unless it’s within minutes of expiration, > otherwise the option would be priced at 0. Options > on index futures can have long-dated contracts > that expire almost a decade from now. agree with JTLD. 1 does not make sense.
I would say a nickel.
well yeah, obviously it can’t be 1 exactly, so i shall reiterate. for a 70 yr. call option, delta = 0.97-0.999. b/c the incremental downside volatility is mostly negligable and the relative upside btw the option and stock should mostly be the same b/c of the EV of the stock itself 70 years from now.
i guess it depends on what this is a call option on… since no one has specified that. im just going off black scholes here but whether or not dividends are paid, especially for the time horizon we’re discussing, could bring the delta from close to 1, to close to 0.
Assuming T >10yrs anywhere between 0 and .5
ZeroBonus is close. The delta for a long-dated at-the-money option will never be close to 1. By definition it has a lot of embedded time premium, and even if the stock is not volatile it can pretty easily trade in a huge range over a long time period so there is a large volatility component. As an example I looked up the longest dated contract for the SPY which is Dec 2011, at-the-money calls are priced via Black-Scholes at about 0.6 delta currently. At-the-money options in general will always be priced near 0.5 unless it is very close to expiration.
I’m not a big option guy, but my understanding is that delta is always 0.5 when the option is at the money. Period.
Thanks man, it took me 5 minutes to type out my response and you come in and repeat it as your own. Welcome back.
the graph of delta for a call option is an increasing function, between 0 and .5 its convex while out of the money, around .5 for at the money and then concave down from .5 to 1 once in the money… however, this does not consider dividends… mirror image for put options thats why delta is negative… on a side note looking at these graphs explains why gamma is always positive and the same for like call and put options… looks like a peak from 0 to 1, the peak is at the strike price im just in a really good mood today.
IheartMath Wrote: ------------------------------------------------------- > im just in a really good mood today. Reason?
But I think for a very long T, delta has to be less than 0.5
I think for a long T, delta would slightly be more then .5 (because of the risk free rate). IBM is 119. Jan 2010 120 Call Delta is .5098 Jan 2011 120 Call Delta is .5383
by long T I meant >10yrs because small price changes have almost little to no impact on the option value.
JohnThainsLimoDriver Wrote: ------------------------------------------------------- > Thanks man, it took me 5 minutes to type out my > response and you come in and repeat it as your > own. Welcome back. Our posts must have crossed. I didn’t see yours. Thanks for the welcome. Brazil was great!
but for example, using $100 SPY options as our case, the range between Dec 2009 and Dec 2010 is $6-$11. Dec 2010 to Dec 2011 is $11-$15. Obviously each additional year will result in less of a premium for that extra year. i guess i’ll be the only one who actually does a calculation. using black-scholes assuming vol = .17, RF = inflation = 3%, t = 70 years; S and K both equal 100. = 100 N(d1) - 100 e^-(0.03)(70) N (d2) N(d1) and N(d2) both equal 0.999. this is where most of the difference lies between a 1 and 2 year option for example, but in this example, 70+ yrs, it makes no difference. = 99.9 - 12.221 = $87.679 if S = $100 and the call option = $87.679, they would move almost entirely in step as every incremental gain made by the stock is inherently an incremental gain in the call option, assuming its american. thus, delta = 0.98+